Phase-field model with plastic flow for grain growth in nanocrystalline material

Abstract

A phase-field model is presented which considers the accumulation of structural defects in grain boundaries by an isotropic eigenstrain associated with the grain boundaries. It is demonstrated that the elastic energy caused by dilatation of the grain boundary with respect to the bulk crystal contributes largely to the grain boundary energy. The sign of this contribution can be both positive and negative dependent on the local stress state in the grain boundary. Self-diffusion of atoms is taken into account to relax the stress caused by the dilatation of the grain boundary. Application of the model to discontinuous grain growth in pure nanocrystalline cobalt material is presented. Linear grain growth is found in the nanocrystalline state, which is explained by the interpretation of grain boundary motion as a diffusive process defining an upper limit of the grain boundary velocity independent of the grain boundary curvature but dependent on temperature. The transition to regular grain growth at a critical temperature, as observed experimentally, is explained by the drop of theoretical grain boundary velocity due to its mean curvature during coarsening of the nanograin structure below the maximum velocity.

Keywords:

• phase-field
• grain growth
• nanocrystalline material

Acknowledgements

I. Steinbach and A. Hartmaier acknowledge support from the sponsors of ICAMS, ThyssenKrupp Steel AG, Salzgitter Mannesmann Forschung GmbH, Robert Bosch GmbH, Bayer Materials Science AG and Bayer Technology Services GmbH, Benteler AG and the state of North Rhine-Westphalia. X. Song thanks the National Natural Science Foundation of China (50871001) for financial support for the experimental work.